Well if you want to try it, just to see if you like the tone you can try this:
But be aware that your PT probably can't can't handle the load and might blow, so if it's getting hot (before you blow up the PT,) touch it, hot, take the 6L6's out.
Raise the cathode bias resistor to 10 watt (250, 10 watt)
Change the rectifier tube to a GZ34 or 5AR4
add screen grid resistors (1K5, 5 watt) don't have to do it just to try
if you have an 8 ohm speaker, use the 16 ohm spk jack with your 8 ohm. 4 ohm use the 8
There are a few power rail resistors to change but you can do that later.
Give it a go, but like Sluckey says you won't get the true headroom you want at least yet
The biggest problem is the PT probably can't handle the 6L6's, and you'll need a bigger PT.
Original OT is too small too, need a 25/30 watt at least
6L6s need a higher voltage, a bigger PT will give that and higher rating will keep it cool (meaning won't blow)
PS "Not responsible for a blown PT"
One other thing: I put switches in my 5E3, 6V6s or 6L6's, with all the "proper changes", new PT and OT, too. Maybe a little more kick and a tad more headroom but not a Deluxe Reverb sound, closer to a 5E3 on small dose of steroids. My switches have been on the 6V6 settings for the last three years and I'll probably take the PT and OT out for another project when I get the time and bug. IMO, really don't brother, BTW, Neil Young runs 6L6's in his, if you like his tone go for it.